1. Field of the Invention
The present invention relates, in general, to balanced modulators and, more particularly, to variable transconductance four-quadrant Gilbert-type modulators with improved linearity and improved carrier suppression.
2. Description of Related Art
Analog modulators and multipliers are well known. One particular type of well known multiplier circuit is a variable-transconductance four-quadrant differential-pair or Gilbert-type multiplier. Such circuits are designed for use where the output of the circuit is a linear product of two input voltages. Typically, the linear product is adjustable by a scale factor. The basic differential-pair multiplier was introduced in B. Gilbert, "A Precise Four-Quadrant Multiplier With Subnanosecond Response," IEEE Journal of Solid State Circuits, SC-3, No. 4, pages 365-367 (December 1968). See also, Clarke et al., Communication Circuits: Analysis And Design (Addison-Wesley Publishing Co. 1971), pages 362-373, for a textbook treatment of the Gilbert-type multiplier. The four-quadrant Gilbert-type multiplier is readily available in integrated circuit form. For example, Motorola Semiconductors produces a four-quadrant multiplier chip known as an MC1595L chip.
Where one input to the above-described variable-transconductance four-quadrant Gilbert-type multiplier is a carrier signal and the other input is a modulation input, the multiplier becomes a useful modulator. Such a modulator is commonly known as a balanced, suppressed carrier, or double sideband modulator as well as a variable-transconductance four-quadrant Gilbert-type modulator. Practical uses of these types of modulators include AM transmission and reception and generation of pulses of modulated radio-frequency ("RF") current in the transmission circuitry of magnetic resonance imaging ("MRI") systems (also known as nuclear magnetic resonance ("NMR") imaging systems). In the MRI system, the modulated RF current is used to generate an alternating magnetic field for the controlled excitation of the nuclei of the body being examined.
A variable-transconductance four-quadrant Gilbert-type modulator is shown in block diagramatic form in FIG. 1 as element 10. Modulation input voltage A(t) is input into modulator 10 at modulation input port 11, and carrier input signal V.sub.c (t) is input at carrier input port 12. The resulting modulated output V.sub.out (t) is produced at modulated output port 13 of modulator 10. Contained in the modulator are differential-transconductance amplifier 14, two fixed current sources 15, current sensing resistor R.sub.1, and variable-transconductance circuitry 16. Differential-transconductance amplifier 14 has input port 17 consisting of two leads for receiving the modulation input voltage, has common port 18 for receiving drive currents from fixed current sources 15, and has output port 19. Differential-transconductance amplifier 14 includes two active devices 20, 21 having their input (20A, 21A), output (20B, 21B), and common (20C, 21C) leads as shown in FIG. 2. Active devices 20, 21 could be, for example, bipolar transistors in which the inputs (20A, 21A) are the bases of the transistors, the outputs (20B, 21B) are the collectors, and the common (20C, 21C) leads are from the emitters. The active devices could also be JFETs, for example, with the gates as inputs, sources as outputs, and drains as commons.
The currents on the input leads to active devices (20, 21) are negligible with respect to the currents on the output and common leads. Thus, the sum of the drive currents provided by fixed current sources 15 into common port 18 equals the sum of the output currents on output port 19 of differential-transconductance amplifier 14. A variation in the modulation input voltage on modulation input port 11 of modulator 10 and, thus, on input port 17 of differential-transconductance amplifier 14 will produce a change in amplifier 14's differential output current on its output port 19.
As shown in FIGS. 1 and 2, current sensing resistor R.sub.1 is connected across the two leads of common port 18 of differential-transconductor amplifier 14 to provide local feedback in modulator 10. As shown in FIG. 3, a single fixed current source 22 can be used with two current sensing resistors having a value of one-half R.sub.1 each to provide the necessary drive currents.
Variable-transconductance circuitry 16 receives the carrier input signal V.sub.c (t) on carrier input port 12 and also receives the differential output current from output port 19 of differential-transconductance amplifier 14. The gain between carrier input and modulated output of variable-transconductance 16 is varied by variable-transconductance circuitry 16's response to the differential output current received from differential-transconductance amplifier 14 thus providing modulation of the carrier input signal.
One specific embodiment of variable-transconductance four-quadrant Gilbert-type modulator 10 is shown in FIG. 4. That circuit schematic is taken from Motorola Semiconductors' "Specifications and Applications Information MC1595L/MC1495L" concerning Motorola's linear four-quadrant multiplier integrated circuit. The complete schematic illustrated in FIG. 4 shows a linearized Gilbert-type multiplier; however, the right-half of the schematic is a common modulator of the type described above and illustrated in FIGS. 1 and 2. The schematic includes designations to show corresponding parts between the block diagramatic parts of modulator 10 in FIG. 1 with those parts in the schematic in FIG. 4. The schematic also contains the integrated circuit pin numbering P1 through P14 for the Motorola MC1595L chip. Furthermore, the schematic of FIG. 4 shows current sensing resistor R.sub.1 added which is not provided on the Motorola chip itself.
The desired modulated output of the modulator is EQU V.sub.out (t)=A(t).times.sin.omega..sub.c t, (1)
where the angular frequency .omega..sub.c is the carrier frequency and A(t) is the modulation signal. The actual input voltages to the modulator are a carrier input signal voltage V.sub.c (t)=V.sub.r sin.omega..sub.c t and a modulation input voltage V.sub.b (t)=A(t). With these input voltages, the ideal modulator output would be EQU V.sub.out =(V.sub.c .times.V.sub.b)/V.sub.m, (2)
where 1/V.sub.m is a scale factor constant which determines the magnitude of the output voltage.
In practice, however, modulators have two significant deficiencies. The non-ideal modulator's deficiencies are a complicated function of the modulator's two inputs A=A(t) and B=V.sub.r sin.omega..sub.c t and can be expressed using a Taylor series expansion as follows: ##EQU1## In the ideal case, k.sub.11 =V.sub.r /V.sub.m and all other k.sub.ij =0.
The more important deficiencies in the non-ideal modulator are non-linearity and carrier feedthrough. A non-linear relationship between the modulation input and the modulated output, particularly at frequencies near the carrier frequency, is of considerable concern. Such non-linearity in an AM transmitter results in distortion in the demodulated signal in the receiver. In an MRI system, the unwanted non-linearity would cause the generation of imprecise pulses of modulated RF current which, in turn, results in imprecise generation of the necessary alternating magnetic field and, therefore, the incorrectly controlled excitation of the nuclei of the body being studied. The end result would be an ill-defined image.
Each of the terms after the first line in equation (3) above can be classified as non-linearity. In a normal case where the modulation signal is a much lower frequency than the carrier frequency (for example, an audio signal for modulation and radio frequency for the carrier), the most important non-linearity terms of equation (3) are those in the second line of the equation. Those terms give the non-linear relationship between the modulation input and the RF output at frequencies near the carrier frequency. The other significant non-linear terms will appear at frequencies far removed from the carrier frequency.
Unwanted carrier feedthrough arises in a modulator where the output voltage Vout is not zero when the modulation input signal A(t) is zero. For example, in the MRI system, with carrier feedthrough the modulator cannot "shut off" the RF excitation of the nuclei completely. In equation (3) above, the k.sub.01 B term is the unwanted carrier feedthrough term. Typically, the contribution from this term in the modulator output voltage can be cancelled by shifting the zero of the modulation input signal A(t) slightly so that the k.sub.01 term is cancelled by the k.sub.11 term. There are, however, usually other mechanisms in a modulator, such as capacitance from the carrier input to the modulated output, which bypass the modulator and cannot be totally cancelled by the shifting of the zero of the modulation input signal.
Another concern arising from the undesired carrier feedthrough appears when the modulation input is a function of time. In such a situation, when a sine wave having a d.c. level of zero is applied to the modulation input, the modulated output at the carrier frequency should be zero giving the desired suppressed carrier attributes of the modulator. However, in the prior art modulators, there is a measured output at the carrier frequency which is a function of the sine wave amplitude of the input even when the d.c. level of the input is accurately set to zero.
Other deviations from the ideal output voltage of a modulator include the d.c. offset term k.sub.00 shown in equation (3), the modulation input feedthrough k.sub.10 term, and the terms in the third line of equation (3). The d.c. offset term k.sub.00 is not usually important since output circuitry after the modulator can contain circuitry which does not respond to d.c. Since the modulation input feedthrough k.sub.10 is far below the carrier frequency and the terms in the third line of equation (3) give outputs close to harmonics of the carrier frequency, all of those terms can be removed by a suitable bandpass filter after the modulator's output. Such a filter would pass only frequencies near the carrier frequency and would reject both low frequencies (d.c. and modulation) and specified high frequencies (harmonics of the carrier frequency).
Even with the use of bandpass filters as discussed above and with the use of zero shifting of the modulation input signal A(t), the existing variable-transconductance four-quadrant Gilbert-type modulators are still effected by unwanted non-linearity and carrier feedthrough in their outputs. Thus, from the above discussion, it should be apparent that there is a great need for an improved balanced modulator in which the problems of undesired non-linearity and carrier feedthrough are alleviated.
It is, thus, intended that the invention provide a variable-transconductance four-quadrant Gilbert-type modulator in which there is improved performance.
Another intent is that the invention provide a balanced modulator in which non-linearity between the modulation input and the modulated output is reduced.
Still another intent is that the invention provide a balanced modulator with reduced carrier feedthrough.
Other intentions and features of the invention will further become apparent with reference to the accompanying drawings and the detailed description of the invention or may be learned by practice of the invention.